Starting from a slender, tapered shard, the shell of the Conus gloriamaris grows gradually outward in a lazy spiral, flaring out as it wraps itself in layer after layer of gleaming tan-and-white marbling. The meticulous design of a seashell has long been a source of fascination for mathematicians, but the biological process involved has remained mysterious. Equipped with a new understanding of how mollusks use an extensive network of nerve cells to coordinate precise deposits of shell material and pigment, researchers can now simulate the growth of almost any seashell on a computer. And while this may delight molluscophiles, the significance is broad: This advance marks a triumphant cross-pollination between mathematics and biology that is also yielding important insights into how complex neural networks interact and communicate.

Image courtesy Alistair Boettiger

In the 80s, George Oster, a biophysicist at the University of California at Berkeley, and Bard Ermentrout, a mathematician at the University of Pittsburgh, developed a model for seashell growth and pigmentation based on the premise that a highly interconnected network of neurons controls the process. Unfortunately, Oster and Ermentrout lacked sufficient experimental evidence to confirm their theory. German researcher Hans Meinhardt found some success using an alternative model in which secreted chemicals that diffuse throughout the mollusk’s mantle — a tongue-like protrusion responsible for shell construction — govern these activities and turn pigment production on or off in different cells. But the results weren’t completely satisfactory. “Meinhardt could write these models that would produce beautiful pictures of shells,” says Oster. “The only problem is, he had to have a different model for every shell, and nobody has ever found these diffusing and reacting substances.”

More recent experimental findings have given new life to the neurosecretory model, however, including recent findings suggesting that the mantle uses pigment patterns in the shell as a “diary” of past shell-building activity. During shell construction, the mantle is always extended just a bit beyond the lip of the shell, inspecting its prior handiwork; Oster and Ermentrout hypothesized that pigment patterns from days past are scanned and interpreted by the mantle’s nerve network, triggering waves of excitation and inhibition that yield detailed instructions for the next round of construction. “What the mantle is doing is ‘tasting’ back in time,” says Oster, “so it can predict what it should do the next day and so that the pattern will be continuous.”

By charting these discrete patterns of neural excitation and inhibition, Oster and Ermentrout were able to build a mathematical model for shell formation that accounts for virtually any design observed in nature, from the zigzagging lines of Natica communis to the seemingly random patterns of mottled patches on a cone snail’s shell. “A single equation is sufficient to explain this tremendous diversity of patterns,” says Alistair Boettiger, a Berkeley graduate student who developed a computational modeling program for Oster and Ermentrout based on their findings. The team has modeled more than 30 shell types, and in each case the simulation bears a striking resemblance to the real thing. The program is even able to compensate for changes in growth and patterning caused by scratches and scrapes picked up in a mollusk’s tumultuous life at sea.

Just as pioneering experiments with oversize squid neurons in the 1940s and 50s established much of the foundation for modern neuroscience, Oster believes that modeling simple neural processes may have much broader implications for the field. For example, the primitive form of “memory” observed in mollusk neural networks might help researchers to decipher how far more sophisticated networks in the human brain enable us to use prior experience to build a picture of our world. To deepen their understanding, the team is now turning their attention to the cuttlefish, which rapidly changes colors and patterns.. “The patterns are very dynamic, and instead of taking months to form, they do it in a millisecond,” Oster says, “but it’s the same kind of nervous net, and it’s working in very much the same way.”